Extinction time for the weaker of two competing SIS epidemics
| Autor: | Malwina J. Luczak, Fabio Lopes |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Fluid limit education.field_of_study near-critical epidemic Markov chain Differential equation Population Probability (math.PR) 60J27 92D30 time to extinction Fixed point Markov model Stochastic SIS logistic epidemic 60J27 Distribution (mathematics) 92D30 FOS: Mathematics competing SIS epidemics Quantitative Biology::Populations and Evolution Limit (mathematics) Statistical physics Statistics Probability and Uncertainty education Mathematics - Probability Mathematics |
| Zdroj: | Ann. Appl. Probab. 30, no. 6 (2020), 2880-2922 |
| DOI: | 10.48550/arxiv.1802.04037 |
| Popis: | We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic logistic SIS epidemic process, and we assume that there is perfect cross-immunity between the two strains, that is, individuals infected by one are temporarily immune to re-infections and infections by the other. For the case where one strain has a strictly larger basic reproductive ratio than the other, and the stronger strain on its own is supercritical (that is, its basic reproductive ratio is larger than 1), we derive precise asymptotic results for the distribution of the time when the weaker strain disappears from the population, that is, its extinction time. We further extend our results to certain parameter values where the difference between the two reproductive ratios may tend to 0 as $N \to \infty$. In proving our results, we illustrate a new approach to a fluid limit approximation for a sequence of Markov chains in the vicinity of a stable fixed point of the limit. Comment: 53 pages |
| Databáze: | OpenAIRE |
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